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Simplifying 3w2 + 7w + -9 = 0 Reorder the terms: -9 + 7w + 3w2 = 0 Solving -9 + 7w + 3w2 = 0 Solving for variable 'w'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 2.333333333w + w2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.333333333w + 3 + w2 = 0 + 3 Reorder the terms: -3 + 3 + 2.333333333w + w2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.333333333w + w2 = 0 + 3 2.333333333w + w2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.333333333w + w2 = 3 The w term is 2.333333333w. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333w + 1.361111112 + w2 = 3 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333w + w2 = 3 + 1.361111112 Combine like terms: 3 + 1.361111112 = 4.361111112 1.361111112 + 2.333333333w + w2 = 4.361111112 Factor a perfect square on the left side: (w + 1.166666667)(w + 1.166666667) = 4.361111112 Calculate the square root of the right side: 2.088327348 Break this problem into two subproblems by setting (w + 1.166666667) equal to 2.088327348 and -2.088327348.Subproblem 1
w + 1.166666667 = 2.088327348 Simplifying w + 1.166666667 = 2.088327348 Reorder the terms: 1.166666667 + w = 2.088327348 Solving 1.166666667 + w = 2.088327348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + w = 2.088327348 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + w = 2.088327348 + -1.166666667 w = 2.088327348 + -1.166666667 Combine like terms: 2.088327348 + -1.166666667 = 0.921660681 w = 0.921660681 Simplifying w = 0.921660681Subproblem 2
w + 1.166666667 = -2.088327348 Simplifying w + 1.166666667 = -2.088327348 Reorder the terms: 1.166666667 + w = -2.088327348 Solving 1.166666667 + w = -2.088327348 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + w = -2.088327348 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + w = -2.088327348 + -1.166666667 w = -2.088327348 + -1.166666667 Combine like terms: -2.088327348 + -1.166666667 = -3.254994015 w = -3.254994015 Simplifying w = -3.254994015Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.921660681, -3.254994015}
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